Existing reverse-engineering tools use algorithms based on vague and verbose definitions of UML constituents to recover class diagrams from source code. Thus, reverse-engineered class diagrams are neither abstract nor precise representations of source code and are of little interest for software engineers. We propose an exhaustive study of class diagram constituents with respect to their recovery from C++, Java, and Smalltalk source code. We exemplify our study with a tool suite, Ptidej, to reverse-engineer Java programs as UML class diagrams abstractly and precisely. The tool suite produces class diagrams that help software engineers in better understanding programs.